What follows below is the extent of my efforts so far to answer the question of the origins of the name Bogaig. For much of this entry I owe a great debt to Ronnie and Maire Black for their efforts in helping me decipher and understand the relevant ancient Irish language manuscripts. Unfortunately guaranteed proof of the linage and origin of the name is very hard to provide. However, very likely reasoning and strong proof can be.

As with all things in life, it is best to start with what the experts say. In Ireland this means consulting the works of Rev. Patrick Woulfe and Dr. Edward MacLysaght. The entries for both read as follows: Ó Bogaig – Obuge, Buggy; descendants of bogac (derivative of bog, soft, tender) a rare surname[1]
(O) Buggy – ÓBogaigh (bog, soft) An old and well known name in Cos. Wexford and Kilkenny[2]

As most Buggy’s know, Bogaig was the old Irish name that was anglicized to give the modern Irish name of Buggy. According to focal.ie, Bogach, a noun, means soft ground/wetland/boggy depending on the context it is being used in.[3] Bogaig(h) is the genitive plural of Bogach. A number of ancient Irish manuscripts such as The Book of Leinster (MS 1339), The Book of Lecan (MS 23 P 2), The 1467 Manuscript (MS 72.1.1) and The Red Book of Ossory refer to different people with names such as Bacach, Bogaig, Bocaig, Bacaig etc..

We start with The Book of Lecan which was written between 1397-1418. It contains writings from a number of previous manuscripts, including the Book of Leinster. Folio 81r contains a section that discusses Highland genealogy from Scotland (fada’s not included): [4]

This is translated as ‘John and Sorley and Alan and Alexander were the four sons of John son of Alexander son of John son of Duncan. The family of Eoin Bocach up to that point.’[5] This section and Eoin Bocaig can be seen below.

There is confusion and debate as to the exact linage of this Eoin Bocaig person. However, that is not the concern of this blog. This same linage also appears in The 1467 Manuscript. However, here he is listed as Eoin Bogaig.

The 1467 Manuscript was written in 1467 and based on what I have found so far, this is the earliest written version of the Bogaig name. This linage was possibly copied from the Book of Lecan linage as Lecan is an older book. It might have been read to the author and this could be the reason for the different spelling.[6] Therefore, this Bogaig could be a corruption of Bocaig.

The first modern translations of The 1467 Manscript were carried out by William Forbes Skene in two 19th century Scottish publications: (i) Collectanea de Rebus Albanicis: Consisting of Original Papers and Documents Relating to the History of the Highlands and Islands of Scotland and (ii)Celtic Scotland: A history of Ancient Alban.[7][8] These entries are taken from page 58 and 59 of Collectanea de Rebus Albanicis:

Skene gives the translation for Eoin Bogaigas Eoin the Lame, bacach being the Irish word for lame.[9] It is important to note that numerous criticisms have been leveled at his translation of the ancient texts by many historians such as Alexander Macbain, George Eyre-Todd and David Sellars. Despite this, bacach (lame) seems to have stuck as a translation for bogaig from ancient texts.

[3] The is the national database of Irish language terminology developed by Dublin City University and Foras na Gaeilge

[4] Early inhabitants of Ireland and Scotland, along with Welsh, Manx and Breton people, were from a common Gaelic race. People from Ireland invaded and inhabited Scotland from the 6th century onwards and a common Irish language was spoken in both up to the Middle Ages and later.

Re: Origin of Irish name OBogaig(h)/Buggy.
When searching, more often than not, one will find: a rare old name probably of English origin, with the examples of Bugg, Buge etc.
I prefer the reference by Brother Cleary, in The Annals of the Four Mastert to: The Breakup of the Parish of Rathdowney in the Dioces of Ossary, as follows.
St. Bridget on her way to Cashel to visit St. Patrick, stayed at the nunnery in Ballybuggy, County Laoise (Leix) in Leinster. Mentioned also was, Ballybuggy, probably was the seat of the surrounding area in earlier times. The conversion of Ireland by St. Patrick date is 432 AD. This establishes the Gaelic name OBogaig, later OBogaig(h), OBuggy, Buggy as, an old Gaelic name centuries before the Anglo influence (perhaps the wrong word) in Ireland.